A spherical initial ideal for Pfaffians
2007 (English)In: Illinois Journal of Mathematics, ISSN 0019-2082, Vol. 51, no 4, 1397-1407 p.Article in journal (Refereed) Published
We determine a term order on the monomials in the variables X-ij, 1 <= i <= j <= n, such that corresponding initial ideal of the ideal of Pfaffians of degree r of a generic n by n skew-symmetric matrix is the Stanley-Reisner ideal of a join of a simplicial sphere and a simplex. Moreover, we demonstrate that the Pfaffians of the 2r by 2r skew-symmetric submatrices form a, Grobner basis for the given term order. The same methods and similar term orders as for the Pfaffians also yield squarefree initial ideals for certain determinantal ideals. Yet, in contrast to the case of Pfaffians, the corresponding simplicial complexes are balls that do not decompose into a join as above.
Place, publisher, year, edition, pages
2007. Vol. 51, no 4, 1397-1407 p.
IdentifiersURN: urn:nbn:se:kth:diva-17242ISI: 000258640700021ScopusID: 2-s2.0-50949087634OAI: oai:DiVA.org:kth-17242DiVA: diva2:335285
QC 201410212010-08-052010-08-052014-10-21Bibliographically approved